$C^0$-limits of Legendrians and positive loops

Georgios Dimitroglou Rizell; Michael G. Sullivan

$C^0$-limits of Legendrians and positive loops

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2212.09190 v4 pith:3R4B4HQW submitted 2022-12-18 math.SG

Georgios Dimitroglou Rizell , Michael G. Sullivan This is my paper · ORCID

classification math.SG

keywords submanifoldimagelegendrianpositiveadmitschekanov--hofer--shelukhincontactcontactomorphisms

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

We show that the image of a Legendrian submanifold under a homeomorphism that is the $C^0$-limit of a sequence of contactomorphisms is again Legendrian, if the image of the submanifold is smooth. In proving this, we show that any non-Legendrian submanifold of a contact manifold admits a positive loop and we provide a parametric refinement of the Rosen--Zhang result on the degeneracy of the Chekanov--Hofer--Shelukhin pseudo-norm for non-Legendrians.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On certain $C^0$-aspects of contactomorphism groups
math.SG 2024-11 accept novelty 8.0 of 10

Contactomorphism groups of R^{2n+1} admit a dense conjugacy class, those of R^{2n}×S^1 do not, and Sandon's spectral norm is C^0-locally bounded and extendable to the C^0-closure.

Pith tools